Quantum simulation of molecules without fermionic encoding of the wave function

Molecular simulations generally require fermionic encoding in which fermion statistics are encoded into the qubit representation of the wave function. Recent calculations suggest that fermionic encoding of the wave function can be bypassed, leading to more efficient quantum computations. Here we show that the two-electron reduced density matrix (2-RDM) can be expressed as a unique functional of the unencoded N-qubit-particle wave function without approximation, and hence, the energy can be expressed as a functional of the 2-RDM without fermionic encoding of the wave function. In contrast to current hardware-efficient methods, the derived functional has a unique, one-to-one (and onto) mapping between the qubit-particle wave functions and 2-RDMs, which avoids the over-parametrization that can lead to optimization difficulties such as barren plateaus. An application to computing the ground-state energy and 2-RDM of H4 is presented.

The coherence of light is fundamentally tied to the quantum coherence of the emitting particle

Coherent emission of light by free charged particles is believed to be successfully captured by classical electromagnetism in all experimental settings. However, recent advances triggered fundamental questions regarding the role of the particle wave function in these processes. Here, we find that even in seemingly classical experimental regimes, light emission is fundamentally tied to the quantum coherence and correlations of the emitting particle. We use quantum electrodynamics to show how the particle’s momentum uncertainty determines the optical coherence of the emitted light. We find that the temporal duration of Cherenkov radiation, envisioned for almost a century as a shock wave of light, is limited by underlying entanglement between the particle and light. Our findings enable new capabilities in electron microscopy for measuring quantum correlations of shaped electrons. Last, we propose new Cherenkov detection schemes, whereby measuring spectral photon autocorrelations can unveil the wave function structure of any charged high-energy particle.

Inelastic Form Factor Calculations for 46,48,50Ti Isotopes Using Tassie Model

Inelastic form factors of electrical transition have been calculated for 46,48,50Ti isotopes using the Tassie model. The form factors have been calculated for different exciting energies. The harmonic oscillator (HO) wave function has been used as a single-particle wave function. The model space has been considered as 1f7/2, 2p3/2, 2p1/2, and 2f5/2. Gx1 has been used as effective interaction in all calculations. In all calculations, the effective charge has been considered as 1.5e for proton and 0.5e for neutron. All obtained results have been compared with data from an experiment. The calculations show the Tassie model gives a good description of longitudinal form factors of 46,48,50Ti isotopes in E(2+) transitions as compared with experimental data, especially in the region below 2 fm−1 of momentum transfer, but in the E(4+), the theoretical results deviated slightly from experimental data especially in the region greater than 1.5 fm−1 of momentum transfer.

Ab Initio Dot Structures Beyond the Lewis Picture

The empirical Lewis picture of the chemical bond dominates the view chemists have of molecules, of their stability and reactivity. Within the mathematical framework of quantum mechanics, all this chemical information is hidden in the many-particle wave function Ψ. Thus, to reveal and understand it, there is great interest in enhancing the Lewis model and connecting it to computable quantities. As has previously been shown, the Lewis picture can often be recovered from the probability density |Ψ|2 with probabilities in agreement with valence bond weights: the structures appear as most likely positions in the all-electron configuration space. Here, we systematically expand this topological probability density analysis to molecules with multiple bonds and lone pairs, employing correlated Slater-Jastrow wave functions. In contrast to earlier studies, non-Lewis structures are obtained that disagree with the prevalent picture and have a potentially better predictive capability. While functional groups are still recovered with these ab initio structures, the boundary between bonds and lone pairs is mostly blurred or non-existent. In order to understand the newly found structures, the Lewis electron pairs are replaced with spin-coupled electron motifs as the fundamental electronic fragment. These electron motifs—which coincide with Lewis’ electron pairs for many single bonds—arise naturally from the generally applicable analysis presented. An attempt is made to rationalize the geometry of the newly-found structures by considering the Coulomb force and the Pauli repulsion.

CLUSTER SHELL MODEL WAVE FUNCTION: STRUCTURE OF 6LI NUCLEUS

In this paper cluster model wave function for 6Li using Shell Model with definite parity and angular momentum is written along with cluster co-ordinates, which are relative to the center-of-mass of various clusters and involve with parameters. These parameters can be adjusted to some extent to obtain predictions close to experimental properties. The cluster model wave function is written along with resonating group method (RGM) and the Complex Generator Coordinate Technique (CGCT). The Complex Generator Coordinate Technique allows the transformation of the cluster model wave function written in terms of cluster co-ordinates into anti-symmetrized product of single particle wave function. This wave function is written in terms of single particle co-ordinates, the center-of-mass co-ordinates, parameter coordinates and generator coordinates.

The Bose-Einstein statistics: Remarks on Debye, Natanson, and Ehrenfest contributions and the emergence of indistinguishability principle for quantum particles

The principal mathematical idea behind the statistical properties of black-body radiation (photons) was introduced already by L. Boltzmann (1877/2015) and used by M. Planck (1900; 1906) to derive the frequency distribution of radiation (Planck’s law) when its discrete (quantum) structure was additionally added to the reasoning. The fundamental physical idea – the principle of indistinguishability of the quanta (photons) – had been somewhat hidden behind the formalism and evolved slowly. Here the role of P. Debye (1910), H. Kamerlingh Onnes and P. Ehrenfest (1914) is briefly elaborated and the crucial role of W. Natanson (1911a; 1911b; 1913) is emphasized. The reintroduction of this Natanson’s statistics by S. N. Bose (1924/2009) for light quanta (called photons since the late 1920s), and its subsequent generalization to material particles by A. Einstein (1924; 1925) is regarded as the most direct and transparent, but involves the concept of grand canonical ensemble of J. W. Gibbs (1902/1981), which in a way obscures the indistinguishability of the particles involved. It was ingeniously reintroduced by P. A. M. Dirac (1926) via postulating (imposing) the transposition symmetry onto the many-particle wave function. The above statements are discussed in this paper, including the recent idea of the author (Spałek 2020) of transformation (transmutation) – under specific conditions – of the indistinguishable particles into the corresponding to them distinguishable quantum particles. The last remark may serve as a form of the author’s post scriptum to the indistinguishability principle.

STUDY OF NUCLEON CORRELATIONS IN HEAVY NUCLEI WITH HIGH ENERGY ELASTIC ELECTRON SCATTERING

During the last decade the detailed analysis of several observables and especially of electron scattering data has shown conclusively the presence of short-range nucleon correlations. As a result the degree to which the shape and amplitude of a correlated wave function can be approximated by an independent particle wave function has emerged as a question of fundamental importance. A presentation will be given below of an experiment that will be performed at the Bates Linear Accelerator Center attempting to study this question. The elastic cross-section ratios from 208,207,206Pb,205Ti(e,e) will be measured with high accuracy up to momentum transfers of 3.4 fm^-1 in order to study the influence of correlations on the shape of the 3s1/2 proton wave function. The purpose, motivation and main aspects of the new research will be explained and the experimental considerations together with the running scenario for the experiment will be presented.

A variational mean-field study of clusterization in a zero-temperature system of soft-core bosons

We work out the ground-state diagram of weakly-repulsive penetrable bosons, using mean-field theory with a Gaussian ansatz on the single-particle wave function. Upon compression, the fluid transforms into a cluster supersolid, whose structure is characterized for various choices of the embedding space. In Euclidean space, the stable crystals are those with the most compact structure, i.e., triangular and fcc in two and three dimensions, respectively. For particles confined in a spherical surface, as the sphere radius increases we observe a sequence of transitions between different cluster phases, all having a regular or semiregular polyhedron as supporting frame for the clusters. The present results are relevant for the behavior of ultracold bosons weakly coupled to a Rydberg state.